THE LOG OF GRAVITY

合集下载

地心引力电影英语介绍

地心引力电影英语介绍In the vast expanse of the universe, where the only constant is change, "Gravity" takes us on a breathtaking journey into the unknown. Directed by Alfonso Cuarón and starring Sandra Bullock and George Clooney, this film is a testament to the resilience of the human spirit in the face of insurmountable challenges. Set in a bleak and desolate space environment, "Gravity" tells a story of survival against all odds.The film opens with a devastating accident on the International Space Station (ISS). A chain reaction of explosions tears through the station, leaving Bullock's character, Dr. Ryan Stone, and Clooney's character, Matt Kowalski, stranded in space with limited resources and no hope of rescue. As they struggle to survive, the film captures the stark beauty and terrifying isolation of space, making the viewer feel the weightlessness and helplessnessof their situation.Ryan and Kowalski's journey is filled with heart-pounding moments of danger and despair. They must navigate through a debris field, avoid colliding with floatingsatellites and spacecraft, and even face the challenges of space sickness and oxygen depletion. Throughout their ordeal, they rely on each other for support, showing the strength of human bonds in the face of adversity.The cinematography in "Gravity" is breathtaking, capturing the vastness of space and the minuteness of human existence in comparison. The use of 3D technology adds to the immersion, making the viewer feel as if they arefloating alongside Ryan and Kowalski. The sound design is also impeccable, with the silence of space broken only by the occasional beep of a spacecraft or the rush of air as the characters move through their environment.Bullock's performance is the emotional core of the film. Her portrayal of Ryan Stone, a medical engineer turned reluctant astronaut, is both vulnerable and resilient. She captures the panic and terror of being alone in space, as well as the determination and courage it takes to face such impossible odds. Clooney, as Kowalski, provides the comic relief and wisdom needed to balance out the film's tense atmosphere."Gravity" is not just a film about survival in space;it's a film about survival within oneself. It explores themes of fear, loneliness, and the will to live, askingthe viewer to consider what they would do in such a dire situation. The film's message is one of hope and perseverance, reminding us that no matter how dire the situation, the human spirit will always find a way to persevere.In conclusion, "Gravity" is a masterful film that combines breathtaking cinematography, heart-pounding action, and profound themes of human resilience. It is a must-seefor anyone who loves the thrill of adventure and the powerof human spirit.**地心引力：惊心动魄的太空之旅**在宇宙的无垠广阔中，唯一不变的就是变化本身。

GravityModel

The Gravity Model∗James E.AndersonBoston College and NBERJanuary18,2011AbstractGravity has long been one of the most successful empirical models in economics.In-corporating deeper theoretical foundations of gravity into recent practice has led toa richer and more accurate estimation and interpretation of the spatial relations de-scribed by gravity.Wider acceptance has followed.Recent developments are reviewedhere and suggestions are made for promising future research.JEL Classiﬁcation:F10,R1.Contact information:James E.Anderson,Department of Economics,Boston Col-lege,Chestnut Hill,MA02467,USA.Keywords:Incidence,multilateral resistance,trade costs,migration.∗This review was prepared for Annual Review of Economics,vol.3.I thank Jeﬀrey H.Bergstrand,Keith Head,J.Peter Neary and Yoto V.Yotov for helpful comments.The gravity model in economics was until relatively recently an intellectual orphan,un-connected to the rich family of economic theory.This review is a tale of the orphan’s reunion with its heritage and the beneﬁts that continue toﬂow from connections to more distant relatives.Gravity has long been one of the most successful empirical models in economics,order-ing remarkably well the enormous observed variation in economic interaction across space in both trade and factor movements.The goodﬁt and relatively tight clustering of coeﬃ-cient estimates in the vast empirical literature suggested that some underlying economic law must be at work,but in the absence of an accepted connection to economic theory,most economists ignored gravity.The authoritative survey of Leamer and Levinsohn(1995)cap-tures the mid-90’s state of professional thinking:“These estimates of gravity have been both singularly successful and singularly unsuccessful.They have produced some of the clearest and most robust empiricalﬁndings in economics.But,paradoxically,they have had virtually no eﬀect on the subject of international economics.Textbooks continue to be written and courses designed without any explicit references to distance,but with the very strange im-plicit assumption that countries are both inﬁnitely far apart and inﬁnitely close,the former referring to factors and the latter to commodities.”Subsequently,gravityﬁrst appeared in textbooks in2004(Feenstra,2004),following on success in connecting gravity to economic theory,the subject of Section3.Reviews are not intended to be surveys.My take on the gravity model,thus licensed to be idiosyncratic,scants or omits some topics that others have found important while it emphasizes some topics that others have scanted.My emphases and omissions are intended to guide the orphan to maturity.An adoptive parent’s biases may have contaminated my judgment,caveat emptor.My focus is on theory.Incorporating the theoretical foundations of gravity into recent practice has led to richer and more accurate estimation and interpretation of the spatial relations described by gravity,so where appropriate I will point out this beneﬁt.The har-vest reaped from empirical work applying the gravity model is recently surveyed elsewhere (Anderson and van Wincoop,2004;Bergstrand and Egger,2011).From a modeling standpoint,gravity is distinguished by its parsimonious and tractable representation of economic interaction in a many country world.Most international economic theory is concentrated on two country cases,occasionally extended to three country cases with special features.The tractability of gravity in the many country case is due to its modularity:the distribution of goods or factors across space is determined by gravity forces conditional on the size of economic activities at each location.Modularity readily allows for disaggregation by goods or regions at any scale and permits inference about trade costs not dependent on any particular model of production and market structure in full general equilibrium.The modularity theme recurs often below,but is missing from some other prominent treatments of gravity in the literature.1Traditional GravityThe story begins by setting out the traditional gravity model and noting clues to its union with economic theory.The traditional gravity model drew on analogy with Newton’s Law of Gravitation.A mass of goods or labor or other factors of production supplied at origin i,Y i, is attracted to a mass of demand for goods or labor at destination j,E j,but the potential ﬂow is reduced by the distance between them,d ij.Strictly applying the analogy,X ij=Y i E j/d2ijgives the predicted movement of goods or labor between i and j,X ij.Ravenstein(1889) pioneered the use of gravity for migration patterns in the19th century UK.Tinbergen(1962) was theﬁrst to use gravity to explain tradeﬂows.Departing from strict analogy,traditional gravity allowed the exponents of1applied to the mass variables and of−2applied to bilateral distance to be generated by data toﬁt a statistically inferred log-linear relationship betweendata onﬂows and the mass variables and distance.Generally,across many applications,the estimated coeﬃcients on the mass variables cluster close to1and the distance coeﬃcients cluster close to−1while the estimated equationﬁts the data well:most data points cluster close to theﬁtted line in the sense that80−90%of the variation in theﬂows is captured by theﬁtted relationship.Theﬁt of traditional gravity improved when supplemented with other proxies for trade frictions,such as the eﬀect of political borders and common language.Notice that bilateral frictions alone would appear to be inadequate to fully explain the eﬀects of trade frictions on bilateral trade,because the sale from i to j is inﬂuenced by the resistance to movement on i’s other alternative destinations and by the resistance on move-ment to j from j’s alternative sources of supply.Prodded by this intuition the traditional gravity literature recently developed remoteness indexes of each country’s‘average’eﬀectivedistance to or from its partners(id ij/Y i was commonly deﬁned as the remoteness of coun-try j)and used them as further explanatory variables in the traditional gravity model,with some statistical success.The general problem posed by the intuition behind remoteness indexes is analogous to the N-body problem in Newtonian gravitation.An economic theory of gravity is required for an adequate solution.Because there are many origins and many destinations in any application,a theory of the bilateralﬂows must account for the relative attractiveness of origin-destination pairs.Each sale has multiple possible destinations and each purchase has multiple possible origins:any bilateral sale interacts with all others and involves all other bilateral frictions.This general equilibrium problem is neatly solved with structural gravity models.For expositional ease,the discussion focuses below on goods movements except when migration or investment is speciﬁcally treated.2Frictionless Gravity LessonsTaking a step toward structure,an intuitively appealing starting point is the description of a completely smooth homogeneous world in which all frictions disappear.Developing the implications of this structure yields a number of useful insights about the pattern of world trade.A frictionless world implies that each good has the same price everywhere.In a homoge-neous world,economic agents everywhere might be predicted to purchase goods in the same proportions when faced with the same prices.In the next section the assumptions on pref-erences and/or technology that justify this plausible prediction are the focus,but here the focus is on the implications for trade patterns.In a completely frictionless and homogeneous world,the natural benchmark prediction is that X ij/E j=Y i/Y,the proportion of spending by j on goods from i is equal to the global proportion of spending on goods from i,where Y denotes world spending.Any theory must impose adding up constraints,which for goods requires that the sum of sales to all destinations must equal Y i,the total sales by origin i,and the sum of purchases from all origins must equal E j,the total expenditure for each destination j.Total sales andexpenditures must be equal:i.e.,iY i=jE j=Y.One immediate payoﬀis an implication for inferring trade frictions.Multiplying both sides of the frictionless benchmark prediction X ij/E j=Y i/Y by E j yields predicted friction-less trade Y i E j/Y.The ratio of observed trade X ij to predicted frictionless trade Y i E j/Y represents the eﬀect of frictions along with random inﬂuences.(Bilateral trade data are notoriously rife with measurement error.)Fitting the statistical relationship between the ratio of observed to frictionless trade and various proxies for trade costs is justiﬁed by this simple theoretical structure as a proper focus of empirical gravity models.Thus far,the treatment of tradeﬂows has been of a generic good that most of the literature has implemented as an aggregate:the value of aggregate bilateral trade in goods for example.But the model applies more naturally to disaggregated goods(and factors)becausethe frictions to be analyzed below are likely to diﬀer markedly by product characteristics. The extension to disaggregated goods,indexed by k,is straightforward.X kij =Y kiE kjY k=s kib kjY k.(1)Here s ki =Y ki/Y k is country i’s share of the world’s sales of goods class k and b kj=E kj/Y kis country j’s share of the world spending on k,equal to the world’s sales of k,Y k.The notation and logic also readily apply to the disaggregation of countries into regions, and indeed a prominent portion of the empirical literature has examined bilateralﬂows between city pairs or regions,motivated by the observation that much economic interaction is concentrated at very short distances.The model can interpreted to reﬂect individual decisions aggregated with a probability model;see section5.1below.In aggregate gravity applications(i.e.,most applications),it has been common to use origin and destination mass variables equal to Gross Domestic Product(GDP).This is con-ceptually inappropriate and leads to inaccurate modeling unless the ratio of gross shipments to GDP is constant(in which case the ratio goes into a constant term).A possible direction for aggregate modeling is to convert trade to the same value-added basis as GDP,but this seems more problematic than using disaggregated gravity to explain the pattern of gross shipments and then uniting estimated gravity models within a superstructure to connect to GDP.That is the strategy of the structural gravity model research program reviewed here.Equation(1)generates a number of useful implications.1.Big producers have big market shares everywhere,2.small sellers are more open in the sense of trading more with the rest of the world,3.the world is more open the more similar in size and the more specialized the countriesare,4.the world is more open the greater the number of countries,and5.world openness rises with convergence under the simplifying assumption of balancedtrade.Implication1,that big producers have big market shares everywhere,follows because, reverting to the generic notation and omitting the k superscript,the frictionless gravity prediction is that:X ij/E j=s i.Implication2,that small sellers are more open in the sense of trading more with the rest of the world follows fromi=jX ij/E j=1−Y j/Y=1−s jusingjE j=iY i,which implies balanced trade for the world.Implication3is that the world is more open the more similar in size and the more special-ized the countries are.It is convenient to deﬁne world openness as the ratio of internationalshipments to total shipments,ji=jX ij/Y.Dividing(1)through by Y k and suppressingthe goods index k,world openness is given byji=jX ij/Y=jb j(1−s j)=1−jb j s j.Using standard statistical propertiesj b j s j=Nr bsV ar(s)V ar(b)+1/N,where N is the number of countries or regions,V ar denotes variance,r bs is the correlationcoeﬃcient between b and s and1/N=is i/N=jb j/N,the average share.This equationfollows from the shares summing to one and using standard properties of covariance.Here, V ar(s)and V ar(b)measures size dis-similarity and the correlation of s and b,r bs,is aninverse measure of specialization.Substituting into the expression for world openness:ji=jX ij/Y=1−1/N−Nr bsV ar(s)V ar(b)(2)Implication3follows from equation(2)because on the right-hand side the similarity of country size shrinks the variances while specialization shrinks the correlation r bs.The country-size similarity property has been prominently stressed in the monopolistic competition and trade literature.(It is sometimes taken as evidence for monopolistic com-petition in a sector rather than as a consequence of gravity no matter what explains the pattern of the b’s and s’s.)The specialization property has also been noted in that liter-ature as reﬂecting forces that make for greater net international trade,the absolute value of s j−b j.Making comparisons across goods classes,variation in the right-hand side of(2) results from variation in specialization and in the dispersion of the shipment and expenditure shares.Notice again that the cross-commodity variation in world openness arises here in a frictionless world,a reminder that measures of world home bias in a world with frictions must be evaluated relative to the frictionless world benchmark.Country-size similarity also tends to increase bilateral trade between any pair of countries, all else equal.This point(Bergstrand and Egger,2007)is seen most clearly with aggregate trade that is also balanced,hence s j=b j.Equation(1)can be rewritten asX ij=s iji s ijj(Y i+Y j)2Y,where s iji ≡Y i/(Y i+Y j),the share of i in the joint GDP of i and j.The product s ijis ijjis maximized at s iji =s ijj=1/2,so for given joint GDP size,bilateral trade is increasingin country similarity.(With unbalanced trade or specialization,an analogous similarity property holds for the bilateral similarity of income and expenditure shares.Letγj=E j/Y j. Then the same equation as before holds with the right-hand side multiplied byγj.)A more novel implication of equation(2)is implication4,that world openness is ordinarilyincreasing in the number of countries.Increasing world openness due to a rise in the number of countries reﬂects the property that smaller countries are more naturally open and division makes for more and smaller countries.This eﬀect is seen by diﬀerentiating the left-hand side ofji=jX ij/Y=1−jb j s j,yielding−j(b j ds j+s j db j).Increasing the number of countries tends to imply reducingthe share of each existing country while increasing the share(from zero)of the new country. The preceding diﬀerential expression should thus ordinarily be positive.The qualiﬁcation‘ordinarily’is needed because the pattern of share changes will depend on the underlying structure as revealed by the left-hand side of equation(2).On the one hand,the average share1/N decreases as N rises,raising world openness.On the otherhand,the change in the number of countries will usually change r bsin waysthat depend on the type of country division(or confederation)as well as indirect eﬀects on shares as prices change.(The apparent direct eﬀect of N in theﬁrst term on the right-handside of equation(2)vanishes because1/N scalesV ar(b)V ar(s).)A practical implication of this discussion is that inter-temporal comparisons of ratios of world international trade to world income,to be economically meaningful,should be con-trolled for changes in the size distribution and the number of countries,a correction of large practical importance in the past50to100years.Alternatively,measures of openness meant to reﬂect the eﬀects of trade frictions should be constructed in relation to the frictionless benchmark.Applied to aggregate trade data,gravity yields implication5,that world openness rises with convergence under the simplifying assumption of balanced trade for each country,b j= s j,∀j.The right-hand side of equation(2)becomes NV ar(s)+1/N under balanced trade, and per-capita income convergence lowers V ar(s)toward the variance of population.Baier and Bergstrand(2001)use the convergence property to partially explain postwar growth in world trade/income,ﬁnding relatively little action,although presumably more recent data inﬂuenced by the rise of China and India might give more action.Pointing toward a connection with economic theory,the shares s i and b j and the plau-sible hypothesis of the frictionless model must originate from an underlying structure of preferences and technology.Also,the deviation of observed X ij from the frictionless pre-diction reﬂects frictions as they act on the pattern of purchase decisions of buyers and the sales decisions of sellers,which originate from an underlying structure of preferences and technology.3Structural GravityModeling economies with trade costs works best if it moves backward from the end user. Start by evaluating all goods at user prices,applying demand-side structure to determine the allocation of demand at those prices.Treat all costs incurred between production and end use as being incurred by the supply side of the market,even though there are often signiﬁcant costs directly paid by the user.What matters economically in the end is the full cost between production and end use,and the incidence of that cost on the producer and the end user.Many of these costs are not directly observable,and the empirical gravity literature indicates the total is well in excess of the transportation and insurance costs that are observable(see Anderson and van Wincoop,2004,for a survey of trade costs).The supply side of the market under this approach both produces and distributes the delivered goods,incurring resource costs that are paid by end users.The factor markets for those resources must clear at equilibrium factor prices,determining costs that link to end-user prices.Budget constraints require national factor incomes to pay for national expenditures plus net lending or transfers including remittances.Below the national accounts,individual economic agents also meet budget constraints.Goods markets clear when prices are found such that demand is equal to supply for each good.The full general equilibrium requires a set of bilateral factor prices and bilateral goods prices such that all markets clear and all budget constraints are met.This standard description of general economic equilibrium is too complex to yield some-thing like gravity.A hugely useful simpliﬁcation is modularity,subordinating the economic determination of equilibrium distribution of goods within a class under the superstructure determination of the distribution of production and expenditure between classes of goods. Anderson and van Wincoop(2004)call this property trade separability.Observing that goods are typically supplied from multiple locations,even withinﬁne census commodity classes,it is natural to look for a theoretical structure that justiﬁes grouping in this way. The structural gravity model literature has uncovered two structures that work,one on the demand side and one on the supply side,detailed in sections3.1and3.2.Modularity(trade separability)permits the analyst to focus exclusively on inference about distribution costs from the pattern of distribution of goods(or factors)without having to explain at the same time what determines the total supplies of goods to all destinations or the total demand for goods from all origins.This is a great advantage for two reasons.First, it simpliﬁes the inference task enormously.Second,the inferences about the distribution of goods or factors is consistent with a great many plausible general equilibrium models of national(or regional)production and consumption.Modularity also requires a restriction on trade costs,so that only the national aggregate burden of trade costs within a goods class matters for allocation between classes.The most popular way to meet this requirement is to restrict the trade costs so that the distribution of goods uses resources in the same proportion as the production of those same goods.Samuel-son(1952)invented iceberg melting trade costs in which the trade costs were proportional to the volume shipped,as the amount melted from the iceberg is proportional to its volume. The iceberg metaphor still applies when allowing for aﬁxed cost,as if a chunk of the ice-berg breaks oﬀas it parts from the mother glacier.Mathematically,the generalized iceberg trade cost is linear in the volume shipped.Economically,distribution continues to require resources to be used in the same proportion as in production.Fixed costs are realistic and potentially play an important role in explaining why many potential bilateralﬂows are equalto zero.More general nonlinear trade cost functions continue to satisfy the production propor-tionality restriction and thus meet the requirements of modularity,but depart from the iceberg metaphor.Bergstrand(1985)derived a joint cost function that is homogeneous of degree one with Constant Elasticity of Transformation(CET).This setup allows for substi-tution eﬀects in costs between destinations rather than the cost independence due toﬁxed coeﬃcients in the iceberg model.Bilateral costs have a natural aggregator that is an iceberg cost facing monopolistically competitiveﬁrms.A nice feature of the joint cost model is its econometric tractability under the hypothesis of proﬁt maximizing choice of destinations. Although potentially more realistic,the joint cost reﬁnement turns out to make relatively little diﬀerence empirically.Arkolakis(2008)develops a nonlinear(in volume)trade cost function in which hetero-geneous customers are obtained byﬁrms with a marketing technology featuring aﬁxed-cost component(running a national advertisement)and a variable-cost component(leaﬂetting or telemarketing)subject to diminishing returns as the less likely customers are encountered. Because of the Ricardian production and distribution technology,resource requirements in distribution remain proportional to production resource requirements.Arkolakis shows that the marketing technology model can rationalize features of theﬁrm-level bilateral shipments data that cannot be explained with the linearﬁxed-costs model.His setup is not economet-rically tractable but is readily applicable as a simulation model.In all applications based on the preceding cost functions,proxies for costs are entered in some convenient functional form,usually loglinear in variables such as bilateral distance,con-tiguity,membership of a country,continent or regional trade agreement,common language and common legal traditions.See Anderson and van Wincoop(2004)for more discussion.More generality in trade costs that violates the production proportionality restriction comes at the price of losing modularity.See Matsuyama(2007)for recent exploration of the implications of non-iceberg trade costs in a2country Ricardian model.See Deardorﬀ(1980)for a very general treatment of the resource requirements of trade costs as a setting for his demonstration that the law of comparative advantage holds quite generally.3.1Demand-Side StructureThe second requirement for modularity can be met by restricting the preferences and/or technology such that the cross eﬀects in demand between classes of goods(either interme-diate orﬁnal)ﬂow only through aggregate price indexes.This demand property is satisﬁed when preferences or technology are homothetic and weakly separable with respect to a par-tition into classes whose members are deﬁned by location,a partition structure called the Armington assumption.Thus for example steel products from all countries are members of the steel class.Notice that the assumption implies that goods are purchased from multiple sources because they are evaluated diﬀerently by end users,and goods are diﬀerentiated by place of origin.It is usual to impose identical preferences across countries.Diﬀerences in demand across countries,such as a home bias in favor of locally produced goods,can be accommodated, understanding that‘trade costs’now include the eﬀect of a demand side home bias.In practice it is very diﬃcult to distinguish demand-side home bias from the eﬀect of trade costs, since the proxies used in the literature(common language,former colonial ties,or internal trade dummies,etc.)plausibly pick up both demand and cost diﬀerences.Henceforth trade cost is used without qualiﬁcation but is understood to potentially reﬂect demand-side home bias.Declines in trade costs can be understood as reﬂecting homogenization of tastes.Separability implies that each goods class has a natural quantity aggregate and a nat-ural price aggregate,with substitution between goods classes occurring as if the quantity aggregates were goods in the standard treatment.The separability assumption implies that national origin expenditure shares within the steel class are not altered by changes in the prices of non-steel products,though of course the aggregate purchase of steel is aﬀected by the aggregate cross eﬀect.Homotheticity ensures that relative demands are functions onlyof relative aggregate prices.Theﬁrst economic foundation for the gravity model was based on specifying the expendi-ture function to be a Constant Elasticity of Substitution(CES)function(Anderson,1979). Expenditure shares in the CES case are given byX ij E j =βi p i t ijP j1−σ(3)where P j is the CES price index,σis the elasticity of substitution parameter,βi is the ‘distribution parameter’for varieties shipped from i,p i is their factory gate price and t ij>1 is the trade cost factor between origin i and destination j.The CES price index is given byP j=i(βi p i t ij)1−σ1/(1−σ).(4)Notice that the same parameters characterize expenditure behavior in all locations;prefer-ences are common across the world by assumption.Notice also that the shares are invariant to income,preferences are homothetic.With frictionless trade,t ij=1,∀(i,j)and therefore all the buyers’shares of good i must equal the sellers share of world sales(at destination prices),Y i/Y.Thus the frictionless benchmark is justiﬁed by assuming identical homothetic preferences.For intermediate goods,the same logic works replacing expenditure shares with cost shares.The‘distribution parameters’βi bear several interpretations.They could be exogenous taste parameters.Alternatively,in applications to monopolistically competitive products,βi is proportional to the number ofﬁrms from i oﬀering distinct varieties(Bergstrand,1989). Countries with more activeﬁrms get bigger weights.In long run monopolistic competition the number ofﬁrms is endogenous.Due toﬁxed entry costs,bigger countries have more active ﬁrms in equilibrium,all else equal.The number of activeﬁrms contributes to determining the Y i’s that are given in the gravity module.The other building block in the structural gravity model is market clearance:at deliveredprices Y i=jX ij.Multiplying both sides of(3)by E j and summing over j yields a solutionforβi p1−σi,βi p1−σi =Y ij(t ij/P j)1−σE j.Deﬁne the denominator asΠ1−σi.Substituting into(3)and(4)yields the structural gravity model:Xij =EjYiYtijPjΠi1−σ(5)(Πi )1−σ=jtijPj1−σEjY(6)(Pj )1−σ=itijΠi.1−σYiY.(7)The second ratio on the right-hand side of(5)is a decreasing function(under the empirically valid restrictionσ>1)of direct bilateral trade costs relative to the product of two indexes of all bilateral trade costs in the system.Anderson and van Wincoop(2003)called the terms P j andΠi inward and outwardmultilateral resistance respectively.Note that{P1−σj ,Π1−σi}can be solved from(6)-(7)forgiven t1−σij’s,E j’s and Y i’s combined with a normalization.1Under the assumption of bilateral trade cost symmetry t ij=t ji,∀i,j and balanced trade E j=Y j,∀j,the natural normalization isΠi=P i.Anderson and van Wincoop estimated their gravity equation for Canada’s provinces and US states with a full information estimator that utilized(7)withΠi=P i. Subsequent research has focused mostly on estimating(5)with directional countryﬁxedeﬀects to control for E j/P1−σj and Y i/Π1−σi.Multilateral resistance is on the face of it an index of inward and outward bilateral trade costs,but because of the simultaneity of the system(6)-(7),all bilateral trade costs in the world contribute to the solution values.This somewhat mysterious structure has a simple1For any solution to the system{P0j ,Π0i},{λP0j,Π0i/λ}is also a solution.Thus a normalization is needed.Anderson and Yotov(2010a)ﬁnd that the system(6)-(7)solves quite quickly,not surprisingly because it is quadratic in the1−σpower transforms of the P’s andΠ’s.。

Guidelines of wind turbine design

Guidelines
for Design of Wind Turbines
A publication from DNV/Risø
Second Edition
Guidelines for Design of Wind Turbines − DNV/Risø
3. External Conditions
u( z) = u* ln z z0
κ
where u* is the frictional velocity, κ = 0.4 is von Karman’s constant, and neutral atmospheric conditions are assumed. The frictional velocity is defined as u* = (τ/ρ)1/2, in which τ is the surface shear stress, and ρ is the air density. For engineering calculations it may sometimes prove useful to apply the following empirical approximation for the scale parameter A
z z0 A = AH H ln z0 ln
where the exponent α depends on the terrain roughness. Note that if the logarithmic and exponential expressions for A given above are combined, a height-dependent expression for the exponent α results

Anton Paar DMA 35 密度测量仪说明书

Portable Density/SpecificGravity/Concentration MeterDMA 35DMA 35 …… talks the same languageYour DMA 35 communicates with you in a language youwill understand immediately. The user interface is clearly arranged and you will intuitively find your way through the menu. The display backlight, which switches on automatically when a new sample is filled, makes sure you clearly see your measuring results even in dark surroundings. The seven large keys enable operation of the instrument even when wearing protective gloves.… denies access to spills and humidity The robust DMA 35 is designed to withstand the rough conditions of industrial and field applications. The leakproof sealed housing keeps humidity out of the electronics and stops pump spills entering the instrument.… saves you time and energyOnce defined, you can choose between up to 20 different customized measuring methods and up to 100 sample IDs for easy identification of samples, users or measuring locations. With a memory capacity for 1024 measurement results including timestamp and sample ID, DMA 35 is prepared for a long working day.… uses wireless technologyDMA 35 prints your measuring results and exchanges data with your PC completely wireless via the integrated IrDA interface. Update your instrument with the latest firmware, export measuring data for archiving purposes or simply write your method list and sample ID list on the PC and import it into your instrument via IrDA.… works at the push of a button Your sample is filled into the measuring cell of DMA35 by simply pushing the lever on the built-in pump. DMA 35 measures the density of your sample or determines concentration using the preinstalled density/ concentration tables. You also have the option of adding up to ten custom functions to the list of measuring units. This is useful if you measure specific samples regularly. … lights up the cellTo obtain accurate measuring results it is essential that your sample is filled into the measuring cell without any gas bubbles. The measuring cell of DMA 35, visible from outside through an inspection window, is equipped with a backlight, making it easy for you to observe the filling process closely.© 2016 A n t o n P a a r G m b H | A l l r i g h t s r e s e r v e d .S p e c i f i c a t i o n s s u b j e c t t o c h a n g e w i t h o u t n o t i c e .C 96I P 001E N -G。

地震勘探专业英语

英文汉译Unconformity不整合2D-seismic二维地震3D-seismic三维地震4D-seismic四维地震Abnormal events异常波Absolute permeability绝对渗透率Absorption吸收Absorption coefficient吸收系数Acceleration of gravity重力加速度Accumulate error累计误差Acoustic impedance波阻抗Acoustic logging声波测井Acoustic impedance声阻抗Acoustic impedance section波阻抗剖面Acoustic impedance section声阻抗剖面Acoustic log声波测井Acoustic variable density logging声波变密度测井Acoustic velocity log声速测井Acoustic wave声波Adachi formulas阿达奇公式Adaptive Deconvolution自适应反褶积Adjacent-bed effect围岩影响Adjugate伴随矩阵Aeolotropy各向异性Aerated layer风化层AGC(automatic gain control)自动增益控制Aggradation加积作用Algorithm算法Alias假频Amplitude振幅Amplitude anomaly振幅异常Amplitude distortion振幅失真Amplitude equalization振幅平衡Amplitude log声波幅度测井Amplitude modulation振幅调制Amplitude of the envelope振幅包络Amplitude recovery真振幅恢复AMT（audiomagnetotelluric method）音频大地电磁法Analog模拟Angle of incidence入射角Angular frequency 角频率Anisotropy各向异性Anticipation function 期望函数anticline背斜构造Aperture time时窗时间API unitＡＰＩ单位Apparent表观值Apparent density视密度Apparent dip视倾角Apparent polarity视极性Apparent resistivity视电阻率Apparent velocity视速度Apparent wavelength视波长Apparent wavenumber视波数Applied geophysics应用地球物理学Archie’s formulas阿尔奇经验公式Areal heterogeneity平面非均质Array排列，组合Arrival波至Asynchronous异步的Attenuation衰减Attribute属性，品质Autoconvolution自褶积Autocorrelation自相关Autocovariancet自协方差Auxiliary key horizon辅助标准层Average平均Average velocity平均速度Average velocity平均速度AVO technique AVO技术Axis轴Azimuth方位角，方位Background背景Balanced section平衡剖面Balancing a survey平差Band频带Band-pass通频带Bandwidth带宽Barrier layer隔层Base lap底超Base line基线Base map草图，底图Base station基点Base-line shift基线偏移Basin盆地bedding层理Bias偏差；偏流；偏压；偏磁Bimodal双峰的Bin面元Binary二进制Binate重采样bipole双极bland zone盲区block数据块borehole televiewer井下电视bouguer anomaly布格异常Bouguer correction布格校正boundary conditionBright spot亮点Bulk porosity总孔隙度caprock盖层Chemical sedimentary rock化学沉积岩Clastic sedimentary rock碎屑沉积岩Clay mineral粘土矿物Clean sandstone model纯砂岩模型CMS（chemical remanent magnetization）化学剩磁Compensate neutron log补偿中子测井Complex cycle复合旋回Comprehensive log interpretation测井资料综合解释Concentric folding同心褶皱Connectivity砂体连通性continuation延拓contour等值线convergence收敛Converted wave转换波convolution褶积Core岩芯corer取芯器，取样器correction校正correlation对比；相关；匹配Correlation coefficient相关系数Correlation filter相关滤波COS （common offset stack）共炮检距叠加Cosine law余弦定理coupling耦合Covariance协方差creep蠕变Critical angle临界角Critical damping临界阻尼Crooked line弯曲线测量Cross十字Cross bedding交错层理Crosscorrelation filter互相关滤波crossplot交会图Cross-section剖面；截面Curie point居里点curl旋度Curvature曲率Curve fitting曲线拟合Cycle skip周波跳跃Cylindrical divergence圆柱状发散datum基准面Decay constant衰减常数Decay curve衰减曲线decimate重采样Decimate重采样Declination磁偏角Decollement滑脱面Decomposition分辨Deconvolution反褶积Delay time延迟时间Demodulation解调Density logging密度测井Density contrast密度差Depositional remanent magnetism沉积剩余磁性Depositional sequence沉积层序Depth map深度图Depth migration深度偏移Depth of investigation勘探深度Development seismic开发地震Development well logging开发测井Diaper底避构造Dielectric log介电常数测井Dielectric consist介电常数Differential差异；差分Differential compaction差异压实作用Diffraction绕射Diffraction stack绕射叠加Digital数字Dim spot暗点Dip倾角Dip angle地层倾角Dip direction地层倾向Dip line倾斜测线Dip moveout倾角时差Dipole偶极Direct detection直接检测Direct problem正问题Direct wave直达波Dirichlet condition狄利赫来条件Discrete fourier transform离散傅里叶变换Disharmonic folding不谐和褶皱Dispersion curve频散曲线Displacement偏离Displacement current位移电流Dissertation Abstracts International国际学位论文文摘Distortion畸变Distributed分布Divergence发散；散度Domain域Dome丘，穹隆Dominant frequency主频Doppler effect多普勒效应Downdip下降，下倾，Downlap下超Drape披盖Drift漂移Drill钻机Dual water model双水模型Dynamic correction动校正Dynamic memory动态存储器Dynamic range动态范围Dynamite烈性硝甘炸药Effective permeability有效渗透率Effective porosity有效孔隙度Eigenvalue特征值Eigenvector特征向量Elastic弹性的Elastic constants弹性常数Elastic deformation弹性常数Elastic impedance波阻抗Elastic limit弹性限度Elastic moduli弹性模量Elastic wave弹性波Electromagnetic propagation log电磁波传播测井Elevation correction高程校正emulate仿真End-on端点放炮Engineering geophysics工程地球物理enthalpy焓entropy熵envelope包络equalization均衡Equipotential surface等位面Event同相轴Expectation期望Exponential decay指数衰减Factor analysis因子分析Fade切除Fan-filter扇形滤波Fast fourier transform快速傅里叶变换fault断层Fault断层Fault bench断阶构造Fault drop落差Fault line断层线Fault surface断层面Fault throw断距feedback反馈Fence diagram栅状图Fence effect栅栏效应Fermat’s principle费马原理Filter滤波器Finite-difference method有限差分法Finite-element method有限元法Firing引爆First break初至Flat spot平点Flattened section已拉平的剖面Flexural-slip folding挠曲滑动褶皱Floating datum浮动基准面Flow chart流程图Flushed zone冲洗带flute切除flux通量Flyer检波器串fold地层褶曲folding褶皱format格式formation地层Formation occurrence地层产状Formation sensitivity储层敏感性Formation strike地层走向Formation evaluation地层评价Formation resistivity factor地层电阻率因子Formation-density log地层密度测井Forward solution正演解four-property relationship四性关系fracture裂缝Fresnel diffraction菲涅尔衍射Gas hydrate天然气水合物geochronology地质年代学geodesy大地测量学Geodetic latitude大地纬度Geodetic reference system大地参考系统Geodynamics project地球动力学研究计划Geographic latitude大地纬度geoid大地水准面Geomagnetic pole地磁极Geomagnetic reversal地磁反转Geometric factor几何因子Geometric spreading几何扩散Geophone检波器Geophone检波器组合Geophone array检波器组合Geophone interval检波距Geophone pattern检波器组合geophysicist地球物理学家Geophysics survey地球物理测量geosyncline地槽Geothermal gradient地热梯度ghost虚反射graben地堑graben地堑gradient梯度gravimeter重力仪Gravitational folding重力褶皱Gravitational potential重力位gravity重力Gravity anomaly 重力异常Gravity reduction重力改正Gravity survey重力测量Grid网格Ground roll地滚波Group interval组距Group velocity群速度Guided wave导波hammer重锤Handshake信息交换harmonic谐波Harmonic function调和函数Head wave首波Heat conductivity热导率high-resolution seismic高分辨率地震Horizontal bedding水平层理Horizontal slice水平切片Horizontal spot平点horst地垒horst地垒Igneous rock火成岩Index bed标准层Induced polarization激发极化Inductance电感induction感应Induction electrical survey感应电测井Induction logging感应测井inductivity磁导率Information extracted信息提取Innerbeded heterogeneity层内非均质Instantaneous frequency瞬时频率Instantaneous phase瞬时相位instruction指令insulator绝缘体Integrated circuit集成电路Integrated geophysics综合地球物理Integration混波Intelligent terminal智能终端intensity强度Intensity of magnetization磁化强度Interactive人机联作Interbed夹层Interbed multiple层间多次波Interbeded heterogeneity层间非均质Intercept distortion截断失真Interpretation解释Invaded zone冲洗带Inverse cycle反旋回Inverse draw逆牵引Inversion problem反问题Key bed标志层Laterolog侧向测井Layer velocity section层速度剖面Layer velocity层速度Level calibration层位标定litho-density log岩性密度测井Log interpretation model测井解释模型Log response equation测井响应方程Logging tool standardization测井仪器标准化logging-constrained reversion测井约束地震反演Logs测井曲线Material balance equation物质平衡方程Metamorphic rock变质岩Microelectrode log微电极测井microfacies沉积微相migrated-stacked section偏移叠加剖面Model of bulk-volume rock岩石体积模型Monoclinal strata单斜层mute切除Natural gamma-ray logging自然伽马测井Natural gamma ray spectral log自然伽马能谱测井normal正断层Normal cycle正旋回Normal draw正牵引Normal fault正断层Normal-moveout corrections正常时差校正Nosing structure鼻状构造Oil layer group油层组Oil sandbody油砂体one-step 3D-migration一步三维偏移Parameter参数permeability渗透率Permeability max-mean ratio渗透率突进系数permeability max-min ratio渗透率级差permeability variation coefficient渗透率变异系数Petrophysical property油层物性phase spectrum相位谱Pinch out地层尖灭Polarity reversal极性反转Pore throat孔隙喉道potential势能Primary pore原生孔隙prospect勘探工区，勘探远景区Prospecting seismology勘探地震学Random随机的Ray tracing射线追踪Reciprocity principle互换定理Reconnaissance踏勘，Recover恢复，还原Recovery收获率Recursive filter递归滤波Reef礁Reflecting point反射点Reflection反射Reflection factor反射系数Reflection character analysis反射波特征分析Reflection coefficient反射系数Reflection polarity反射波极性Reflection strength反射波强度Reflection survey反射波勘探Reflector反射界面Refraction折射Refraction wave折射波Refractive index折射系数，折射率Refractor折射界面，折射层Regression海退Regression analysis回归分析Relative permeability相对渗透率Relaxation time驰豫时间Reserving space储集空间reservoir储集层Reservoir fundamental parameter储集层基本参数Resistivity logging电阻率测井Resistivity index电阻率指数resolution分辨率Resolution分辨率Resonance共振Reverberation鸣震reverse逆断层Reverse fault逆断层RMS(root-mean-square)均方根Rock stratum岩层Rock structure岩石构造Rock texture岩石结构Rotational旋转断层Sample ratio取样间隔Sampling theorem采样定理Sand砂岩Sands group砂层组saturation饱和度scattering散射Seal rock封堵层Secondary pore次生孔隙Secondary field二次场Secondary porosity次生孔隙度Sedimentary cycle沉积旋回Sedimentary facies沉积相Sedimentary rhythm沉积韵律Sedimentary rock沉积岩Seis检波器, 地震检波器seiscrop等时切片图Seislog地震测井seisloop三维测量排列Seismic exploration地震勘探Seismic facies地震相Seismic inversion地震反演Seismic normalization地震正演Seismic wavelet地震子波Seismic datum地震基准面Seismic discontinuity地震不连续面Seismic event地震同相轴Seismic exploration地震勘探Seismic facies地震相Seismic log地震测井Seismic map地震构造图Seismic profile地震剖面Seismic pulse地震脉冲Seismic record地震记录Seismic refraction method地震折射波法Seismic section地震剖面Seismic sequence analysis地震层序分析Seismic stratigraphy地震地层学Seismic survey地震勘探Seismic tomography地震层析seismic-geologic section地震地质剖面seismic-sequent stratigraphy地震层序地层学Seismogram地震记录Seismograph地震仪Seismologist地震学家Seismology地震学sensitivity灵敏度Series of development strata开发层系Shale泥岩Shaly sandstone model泥质砂岩模型Shear wave横波Shielding屏蔽，屏蔽层Shoot爆炸，放炮，激发Signal to noise ratio信噪比Significance level显著性水平Similar folding相似褶皱simulated annealing模拟退火Single layer小层Singularity奇点，奇异点，奇异性Skin depth趋肤深度Smoothing平滑SP(spontaneous potential or self potential )自然电位Spacing电极距，源距Spatial aliasing空间假频Spectrum谱，频谱Spherical球面的Spill point溢出点Spontaneous potential log自然电位测井Spread排列，布置Spreading发散，扩散Stacked section水平叠加剖面stacked-migrated section叠偏剖面Stacking velocity叠加速度Standard标准的Static correction静校正Statistical统计的Storage存储器Storm扰动Strain应变，形变，胁变Strata overlap地层超覆Stratigraphic interpretation地层学解释Stratum loss地层缺失Streamer拖缆Strike slip走向滑动断层Stringer高速薄层Structural geology构造地质Structure构造Superposition叠加定理Supervisor野外监督Suppression压制Surface wave面波Survey测量，勘测，勘探Susceptibility磁化率Synchronous同步的syncline向斜构造Synthetic seismogram合成地震记录Synthetic seismogram合成地震记录Systematic error系统误差TAR（ture-amplitude recovery ）真振幅恢复Tectonic map大地构造图Telluric current大地电流Tensor张量Terrain correction地形校正Thermal conductivity热导率Three instantaneous parameter section三瞬剖面throat eveness coefficient喉道均质系数throat mean喉道平均值throat mid-value喉道中值Thrust fault冲断层Thrust fault逆掩断层Tie-line联接测线Time-distance curve时距曲线Time-slice map等时切片Time-variant时变的Tomography层析成像技术Toplap顶超Topographic correction地形校正Total reflection全反射Trace analysis道分析Trace equalization道均衡Trace gather道集Trace integration道积分Trace inversion道反演Trace sequential道序编排transform转换断层Transform fault转换断层Transformed wave转换波Transgression海侵Transient electromagnetic method瞬变电磁法Transistor晶体管Transmission coefficient透射系数Transverse wave横波Transversely isotropic横向各向同性Trap圈闭Travel path传播路径Tree-dimensional survey三维勘探Trough波谷Truncation error截断误差Tumescence火山隆起two-step 3D-migration二步三维偏移Uncertainty不定性，不确定性，不可靠性Updip上倾放炮Uphole geophone井口检波器Upward continuation向上延拓Valley波谷Variable area变面积Variable density变密度Variance方差Vector矢量Velocity analysis速度分析Velocity inversion速度倒转Velocity layering速度分层Velocity spectrum速度谱Velocity sweeping速度扫描Vibration survey振动测量Vibrator振动器Video display视频显示Virtual memory虚拟存储器Viscoelastic粘弹性的Viscosity粘度，粘滞性Water saturation含水饱和度Wave group波组wave equation波动方程Wave equation migration波动方程偏移Wave impedance波阻抗Wave velocity波速Waveform波形Wavefront波前Wavelet地震子波Wavelet equalization子波均衡Wavelet extraction子波提取Wavelet processing子波处理Wavenumber波数Wavy bedding波状层理Weathering 风化层Weathering风化层，低速带Weathering correction低速带校正Weathering layer风化层，低速带Weathering shot低速带测定Weighted array加权平均加权组合Weighted average加权平均Well logging测井Well logging series测井系列White白噪声White noise level白噪水平Young’s modulus杨氏模量Zero-phase零相位Zoeppritz’s equation佐普里茨方程。

电影地心引力英文介绍（五篇范例）

电影地心引力英文介绍（五篇范例）第一篇：电影地心引力英文介绍电影地心引力英文介绍In short, the new sci-fi thriller Gravity is a film that’s set in space and has only two characters.Most of the time, it focuses on only one of them.How exciting could it be?简而言之，这部最新的科幻惊悚片就是一部只有两位主角的太空电影。

影片大多数时间都聚焦在其中一人身上。

所以，这样一部电影到底能有多大魅力呢？It doesn’t sound promising, but the 90-minute film, as the main character Dr Ryan Stone(Sandra Bullock)says, is “one hell of a ride”.听上去该片并不怎么样，但正如主角瑞安•斯通博士（桑德拉•布洛克饰）说的那样，这部90分钟的电影如同一次“地狱之旅”。

Stone, a NASA engineer who’s on her first voyage into space, is installing a component for the Hubble space telescope.Her guide Matt Kowalsky(George Clooney), a charming and experienced astronaut, loops around her, making small talk with Mission Control back on Earth.The camera pans in director Alfonso Cuaron’s signature long takes, framing Bullock with just the blue orb of the Earth behind her.第一次踏上太空的美国宇航局工程师斯通奉命为哈勃太空望远镜安装配件。

《在月亮下面》-英汉对照

简介太阳是一个巨大的燃烧着的火球。

没有来自太阳的光和热，我们就不能在地球这颗行星上生存。

在这颗行星周围有臭氧层保护着我们免受太阳之火的伤害。

但是如果臭氧层破裂，将会怎样呢？现在臭氧层上已经有了小洞，有人说那些小洞会变得越来越大——直到有一天再没有任何东西挡在我们和太阳的火焰之间。

事情发生在2222年。

地球人制造了AOL——人工臭氧层。

美丽的地球又有了1000年的生命。

树又发芽了，下雨了，河里有了水……但现在是2522年，人工臭氧层已经破裂。

幼嫩的树林开始枯萎，河流也逐渐干涸。

凯和瑞拉从他们的宇宙飞船里看到了这危险的情景，可他们又能做些什么呢？月亮下面的部族里住着他们的朋友，可是路途遥远，而地球首领高格又不肯听从他们的指挥。

本书的作者罗维纳·阿金耶米是英国人。

曾在非洲居住和工作了多年。

现在她在剑桥工作和生活。

1 AOLFive hundred kilometres over Europe，ShipOM-45 moved north．In a room at the backof the ship，Kiah watched the numbers onthe computer in front of him．‘Time for dinner，’Rillasaid．The numbers changed quickly and Kiah's eyes didn't move．Rillawent across the room to his table．Shebegan to watch the numbers，too．‘What's wrong with thesatellite？’she asked．Shewas a beautiful girl，about twenty yearsold，with long black hair and big eyes．‘Nothing's wrong with thesatellite，’Kiah answered quietly．‘It'sthe AOL．’He began to write the numbersin the book on his table．Suddenly，the numbersstopped changing．Kiah looked at Rilla．‘OverEurope，’he said．‘It'shappening．The AOL is breaking up．Thereare big holes in the AOL and they're getting bigger．’‘You're right！Shallwe see Captain Seru now，before dinner？’Kiah stood up．He wasnearly two metres tall，with dark eyesand hair．‘Yes，comeon，’he said．Quickly，they went toCaptain Seru's room．They waited at thedoor．‘Come in！’captainSeru called．She was a little woman witha fat face．‘Come in！Wouldyou like a drink？’‘No，thankyou，’Kiah answered．‘I'dlike you to look at these numbers．’Kiahgave Captain Seru his book．1 人工臭氧层OM-45号宇宙飞船在欧洲上空500公里的高度向北飞行。

地球物理专业英语常用单词

Accuracy 准确度AGC: Automatic gain control. 自动增益控制。

Airy Hypothesis艾里假说alias:假频amplitude spectrum振幅谱antiroots反山根Bouguer anomaly布格异常Bouguer correction布格改正continuation延拓density密度density contrast密度差depth of compensation补偿深度dot chart布点量板double Bouguer correction双重布格改正downward continuation向下延拓elevation correction高程改正field continuation位场延拓figure of the earth大地水准面free-air anomaly自由空间异常free-air correction自由空间改正free oscillation of the earth:地球自由震荡gal伽geodesy:大地测量学geoid大地水准面gradiomanometer压差密度计：gradiometer梯度仪gravimeter重力仪gravitational constant万有引力常数gravity重力gravity anomaly:重力异常gravity meter比重计：gravity reduction:重力改正gravity survey重力调查gravity unit重力单位Gutenberg discontinuity:古登堡不连续面horizontal cylinder水平圆柱体isostasy:地壳均衡说：isostatic correction:均衡改正：latitude correction:纬度改正local gravity局部重力值normal gravity正常重力：Poisson's equation：泊松方程：Pratt hypothesis:普拉特假说second-derivative map:二次微商图：topographic correction地形改正torsion balance扭秤Worden:沃尔登重力仪aeromagnetic航空磁测Airborne magnetometer:航空磁力仪alternating-field demagnetization:交变场退磁：Curie point:居里点declination:磁偏角diurnal variation:日变ferrimagnetism:亚铁磁性：ferromagnetic:铁磁性的field intensity:场强fluxgate magnetometer:磁通门磁力仪gamma:伽马gauss:高斯：geomagnetic pole:地磁极geomagnetic reversal: 地磁极倒转：geomagnetic-variation method:地磁变化法：geometric sounding:电磁几何测深：inclination:倾角inductivity:感应率：local magnetic anomalies:局部磁异常magnetic basement:磁性基底：magnetic dip:磁倾角magnetic disturbance磁扰magnetic equator:地磁赤道magnetic field磁场magnetic flux:磁通量magnetic intensity:磁场强度：magnetic interpretation methods磁测资料解释法magnetic meridian:地磁子午线：magnetic moment:磁矩：magnetic permeability:磁导率：magnetic polarization:磁极化：Magnetic pole:磁极：magnetic storms:磁暴：magnetization:磁化强度magnetometer:磁力仪：nanotesla:纳特斯拉：normal magnetic field:正常磁场oersted:奥斯特paleomagnetism:古地磁学：paramagnetic: 顺磁性的：permeability:磁导率，渗透率：polarity:极性：polarization:极化度，极化，偏振：reduction to the pole化向地磁极归极法：secular variation:长期变化：tesla:特斯拉weber:韦伯apparent resistivity: 视电阻率：conductivity:电导率：current electrode:供电电极：dielectric constant:介电常数：dielectric polarization:电介质极化：dipole array:偶极排列dipole-dipole array:偶极-偶极排列：electrical profiling:电剖面法：electrical sounding电测深electrical survey电法勘探，电测井electric field:电场electric susceptibility:电极化率：electrochemical SP:电化学自然电位：electrode电极：electrode equilibrium potential:电极平衡电位：electrode polarization:电极极化：electrode potential:电极电位electrode resistance:电极电阻：electrolyte:电解质：electromagnetic method:电磁法：electromagnetic spectrum:电磁波谱：electronic电子的ELF:极低频：EM:电磁的：emu:电磁单位：equipotential-line method:等位线法equipotential surface:等位面：far-field:远场：fixed-source method:定源法：free-space field:自由空间场：galvanometer:电流计heat flow unit:热流单位HFU:热流单位：horizontal-dipole sounding水平偶极测深induced polarization:激发极化：infinite electrode:无穷远电极：NMR核磁共振permittivity:电容率：polarization ellipse:极化椭圆：pole-dipole array:单极-偶极排列：pole-pole array:单极-单极排列：Primary field: 一次场：secondary field:二次场：self-potential:自然电位self-potential method:自然电位法skin depth:趋肤深度skin effect:趋肤效应sky wave:天波：sky-wave interference:天波干扰：SP:自然电位：spontaneous potential:自然电位：transient electromagnetic method:瞬变电磁法：abnormal events:异常同相轴absorption:吸收作用：acoustic声学的，声的acoustic impedance:声阻抗，波阻抗：acoustic wave: 声波，地震波：air gun:空气枪：air wave:空气波：angle of incidence:入射角：apparent velocity:视速度：apparent wavelength:视波长：arrival:波至：arrival time波至时间：attenuation:衰减average velocity:平均速度azimuth:方位角binary gain:二进制增益blind zone: 盲区：body waves:体波：break:波跳：buried focus effect:地下焦点效应：cable:电缆：chirp:线性调频脉冲:coefficient of anisotropy:各向异性系数coherence:相干性coherent:相关的：common-depth-point:共深度点：common-depth-point stack:共深度点叠加：common-offset gather:共偏移距道集：common-offset stack:共炮检距叠加（同距叠加）：common-range gather:共炮检距道集（选排）：Common reflection point: 共反射点：compressional wave:压缩波：configuration:排列形式：converted wave:转换波critical angle:临界角critical reflection:临界反射：curved path:弯曲射线路径deconvolution:反褶积：deep seismic sounding: DSS.深地震测深：diffraction: 绕射：diffraction stack:绕射叠加：dilatational wave:膨胀波dispersion:扩散，频散display:显示：diving waves:弓形射线波：Dix formula:Dix公式DSS:深地震测深：dynamic corrections动校正：earthquake:天然地震：earthquake seismology: 天然地震测震学：elastic:弹性的：elastic constants:弹性常数：elastic impedance:弹性阻抗：elastic wave:弹性波：electrodynamic geophone:电动检波器：epicenter:震中：event:同相轴：expanding spread: 扩展排列：extended spread:纵排列fathometer:水深计：Fermat’s principle:费马原理：first arrival:初至：first break:初至波：floating datum: 浮动基准面flute槽focus:震源fold: 覆盖次数format:数据格式：Gardner method:加德纳法：gather:道集：geophone:地震检波器：geophone interval:检波距：ground roll:地滚波：group interval:组合间距：group velocity:群速度：guided wave:导波：hammer冲击锤：head wave:首波：：hodograph:矢端线：Hooke's law:虎克定律：horizontal stacking:水平叠加：Huygens principle:惠更斯原理：impedance:阻抗incident angle:入射角：interval velocity:层速度：Kirchoff diffraction equation:基尔霍夫绕射方程：law of reflection:反射定律：law of refraction:透射定律：least-time path:最短时程：Lg-wave: Lg-波：longitudinal wave:纵波：long-path multiple:全程多次反射波：long wave长波：love wave:勒夫波low-velocity layer:低速层：marker bed:标准层：migration: 偏移，运移：minimum-phase:最小相位：multiple:多次波：multiple coverage:多次覆盖：multiplex:多路传输，多倍仪multiplexed format:多路编排格式：mute:切除：NMO: Normal moveout.正常时差。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

models are severely biased, distorting the interpretation of the model. These biases might be critical for the comparative assessment of competing economic theories, as well as for the evaluation of the effects of different policies. In contrast, our method is robust to the different patterns of heteroskedasticity considered in the simulations.
Our estimation method paints a very different picture of the determinants of international trade. In the traditional gravity equation, the coefﬁcients on GDP are not, as generally estimated, close to 1. Instead, they are signiﬁcantly smaller, which might help reconcile the gravity equation with the observation that the trade-to-GDP ratio decreases with increasing total GDP (or, in other words, that smaller countries tend to be more open to international trade). In addition, OLS greatly exaggerates the roles of colonial ties and geographical proximity.
THE LOG OF GRAVITY
J. M. C. Santos Silva and Silvana Tenreyro*
Abstract—Although economists have long been aware of Jensen’s inequality, many econometric applications have neglected an important implication of it: under heteroskedasticity, the parameters of loglinearized models estimated by OLS lead to biased estimates of the true elasticities. We explain why this problem arises and propose an appropriate estimator. Our criticism of conventional practices and the proposed solution extend to a broad range of applications where log-linearized equations are estimated. We develop the argument using one particular illustration, the gravity equation for trade. We ﬁnd signiﬁcant differences between estimates obtained with the proposed estimator and those obtained with the traditional method.
Although many authors have addressed the problem of obtaining consistent estimates of the conditional mean of the dependent variable when the model is estimated in the log linear form (see, for example, Goldberger, 1968; Manning & Mullahy, 2001), we were unable to ﬁnd any reference in the literature to the potential bias of the elasticities estimated using the log linear model.
Using the Anderson–van Wincoop (2003) gravity equation, we ﬁnd that OLS yields signiﬁcantly larger effects for geographical distance. The estimated elasticity obtained from the log-linearized equation is almost twice as large as that predicted by PML. OLS also predicts a large role for common colonial ties, implying that sharing a common colonial history practically doubles bilateral trade. In contrast, the proposed PML estimator leads to a statistically and economically insigniﬁcant effect.
Received for publication March 29, 2004. Revision accepted for publication September 13, 2005.
* ISEG/Universidade Te´cnica de Lisboa and CEMAPRE; and London School of Economics, CEP, and CEPR, respectively.
I. Introduction
ECONOMISTS have long been aware that Jensen’s inequality implies that E(ln y) ln E(y), that is, the expected value of the logarithm of a random variable is different from the logarithm of its expected value. This basic fact, however, has been neglected in many econometric applications. Indeed, one important implication of Jensen’s inequality is that the standard practice of interpreting the parameters of log-linearized models estimated by ordinary least squares (OLS) as elasticities can be highly misleading in the presence of heteroskedasticity.
We next use the proposed method to provide new estimates of the gravity equation in cross-sectional data. Using standard tests, we show that heteroskedasticity is indeed a severe problem, both in the traditional gravity equation introduced by Tinbergen (1962), and in a gravity equation that takes into account multilateral resistance terms or ﬁxed effects, as suggeste We then compare the estimates obtained with the proposed PML estimator with those generated by OLS in the log linear speciﬁcation, using both the traditional and the ﬁxedeffects gravity equations.
Using Monte Carlo simulations, we compare the performance of our estimator with that of OLS (in the log linear speciﬁcation). The results are striking. In the presence of heteroskedasticity, estimates obtained using log-linearized
We are grateful to two anonymous referees for their constructive comments and suggestions. We also thank Francesco Caselli, Kevin Denny, Juan Carlos Hallak, Daniel Mota, John Mullahy, Paulo Parente, Manuela Simarro, and Kim Underhill for helpful advice on previous versions of this paper. The usual disclaimer applies. Jiaying Huang provided excellent research assistance. Santos Silva gratefully acknowledges the partial ﬁnancial support from Fundac¸a˜o para a Cieˆncia e Tecnologia, program POCTI, partially funded by FEDER. A previous version of this paper circulated as “Gravity-Defying Trade.”